Archive for the ‘Non-linearity’ Category

Via a post at the always terrific Watts Up with That, a pre publication version of this paper examines the non-linear coupling dynamics of the climate. Its hypothesis is based on the mathematics of synchronized chaos (sorry, no good introductory link available).

Via Tyler Cowen at Marginal Revolution, an excellent article in Wired about how one formula, embodying one assumption, catalyzed the meltdown. I recommend you read it and ponder it. There are many useful lessons for modeling complex systems in general.

However, I will summarize for those of you short on time. A fundamental problem in securitization is figuring out how different components of a security are related. Think of it as measuring how well the components are diversified. The more independent the components, the less risk embodied in the security. Thus AAA rated tranches of mortgage-backed securities are supposed to be very safe because the components are supposed to be highly independent.

A Chinese mathematician named David X. Li had an insight. You don’t have to analyze the dependencies directly, you just have to observe the correlations in the market prices of the components. Then you can compute these really tight sounding confidence intervals on the correlations of various components because you have all this market data. Of course, the market can’t take into account what it doesn’t understand. So you see a bunch of 25-sigma events. At least, your model says they are 25-sigma. Oops!

I attended the Singularity Summit today. Overall, it was worth the time spent. I did not attend the workshop on Friday because it didn’t look substantive when I reviewed the program. Today, I spoke to several people who were there and they confirmed my prediction. I took 7 pages of notes at the summit and hope to have some insightful synthesis of the material in a few days [Edit: first thought here, more here]. In the meantime, here is a short review of the talks.

I apologize for the posting lull. I actually spotted an issue than I wanted to address a few weeks ago, but I’ve been pondering how to approach it. It’s pretty complicated and subtle. I even ran a couple of drafts by Rafe to refine my thinking. So please bear with me.

As I’ve mentioned before, I am a fan of Dave Zetland. When I saw him propagate what I think is a fundamentally false dichotomy in this post, I knew I had to take on the concept of Knightian uncertainty. It crops up rather often in discussions of forecasting complex systems and I think a lot of people use it as a cop out.